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For a prime 2, let  n  be a positive integer, and  F 2 n be the finite field with 2 n elements. In this paper, we propose several classes of permutation polynomials with the form ( x k +  x ) s +  x 2 n −2  over finite fields  F 2 n which have the highest degree of algebra.

Some classes of permutation polynomials with the form (xk + x) s + x 2 n −2